Structure and Dynamics of Rotating Turbulence: A Review of Recent Experimental and Numerical Results

Godeferd, Fabien S.; Moisy, Frédéric

doi:10.1115/1.4029006

Cited by 82 publications

(84 citation statements)

References 80 publications

(133 reference statements)

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“…Using a penalization technique the nonhomogeneous precession term d(Ω × r)/dt can be taken into account exactly [25]. Another potential source of spurious effects is due to periodic boundary conditions, which force the large-scale columns to wrap around the lattice, something that would not be possible in presence of a solid boundary [26]. The robustness of these approximations will be quantified in a study presented elsewhere.…”

Section: Discussionmentioning

confidence: 99%

Rotating turbulence under “precession-like” perturbation

et al. 2015

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Abstract. The effects of changing the orientation of the rotation axis on homogeneous turbulence is considered. We perform direct numerical simulations on a periodic box of 1024 3 grid points, where the orientation of the rotation axis is changed (a) at a fixed time instant (b) regularly at time intervals commensurate with the rotation time scale. The former is characterized by a dominant inverse energy cascade whereas in the latter, the inverse cascade is stymied due to the recurrent changes in the rotation axis resulting in a strong forward energy transfer and large scale structures that resemble those of isotropic turbulence.PACS. PACS-key discribing text of that key -PACS-key discribing text of that key

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Section: Discussionmentioning

confidence: 99%

Rotating turbulence under “precession-like” perturbation

et al. 2015

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“…Barker and Lithwick [19], in their local model of the elliptical instability, nonetheless showed that strong geostrophic flows emerge during the saturation and disrupt the inertial wave resonances, leading instead to growth and decay cycles. This competition between dominant geostrophic modes and inertial waves is reminiscent of the duality observed in rotating turbulence where, on one hand, geostrophic flows are widely observed [30], and on the other hand, inertial waves have been shown to survive on top of the turbulent background [31][32][33][34]. Conversely from experiments and numerical simulations of rotating turbulence, where energy is injected arbitrarily into both vortices and inertial waves through an external artificial forcing, the elliptical instability provides a natural mechanism that initially injects energy into a few inertial waves only, whose properties can be theoretically predicted.…”

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Inertial Wave Turbulence Driven by Elliptical Instability

et al. 2017

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The combination of elliptical deformation of streamlines and vorticity can lead to the destabilization of any rotating flow via the elliptical instability. Such a mechanism has been invoked as a possible source of turbulence in planetary cores subject to tidal deformations. The saturation of the elliptical instability has been shown to generate turbulence composed of nonlinearly interacting waves and strong columnar vortices with varying respective amplitudes, depending on the control parameters and geometry. In this Letter, we present a suite of numerical simulations to investigate the saturation and the transition from vortex-dominated to wave-dominated regimes. This is achieved by simulating the growth and saturation of the elliptical instability in an idealized triply periodic domain, adding a frictional damping to the geostrophic component only, to mimic its interaction with boundaries. We reproduce several experimental observations within one idealized local model and complement them by reaching more extreme flow parameters. In particular, a wave-dominated regime that exhibits many signatures of inertial wave turbulence is characterized for the first time. This regime is expected in planetary interiors.

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“…The two-dimensionalization and the cyclone-anticyclone asymmetry depend on the external forces and the boundary conditions (e.g., Ref. [9]). …”

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Hysteretic transitions between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence

Yokoyama

Takaoka

2017

Phys. Rev. Fluids

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Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in quasi-two-dimensional (Q2D) flow, while a small rotation rate allows turbulence to be three-dimensional (3D). It is found that the transition from the Q2D turbulent flow to the 3D turbulent flow and the reverse transition occur at different values of the rotation rates. At the intermediate rotation rates, bistability of these two statistically steady states is observed. Such hysteretic behavior is also observed for the variation of the amplitude of an external force.Formation of columnar structures parallel to a rotation axis is one of the most fundamental and distinctive phenomena in flows subject to rotation. The emergence of columnar vortices in the rotating turbulence makes a threedimensional (3D) flow into a quasi-two-dimensional (Q2D) flow. The Taylor-Proudman theorem has succeeded in explaining the cylindrical flow in laboratory experiments and field observations in terms of the Taylor column. However, the theorem cannot describe transitions between the Q2D and 3D flows, because energy is exchanged between the Q2D mode and the 3D mode by nonlinear mechanisms [1]. The energy transfers to the Q2D modes were demonstrated by an instability analysis [2] and weak-turbulence theory in the large-rotation limit [3]. The Coriolis term breaks the parity invariance of the governing equation of the flow, and introduces a scale-independent time scale which induces two-dimensionalization at larger scales more effectively. Therefore, the Coriolis effect originates cyclone-anticyclone asymmetry with enhanced stretching of cyclonic vorticity and destabilization of anticyclonic one due to the centrifugal instability and the vortex tilting [4].To classify the flow properties in rotating systems, the Rossby number Ro, which is the ratio between the linear and nonlinear time scales, has been used [5]. Note that though various definitions of Ro are used in literature, the following facts are independent of its detailed definition. When the Coriolis force is weak relative to turbulence, i.e., Ro ≫ 1, the 3D Kolmogorov turbulence is obtained. When Ro ∼ 1, only cyclonic vortices appear at large scales, and the flow becomes Q2D. When Ro ≪ 1, both cyclonic and anticyclonic vortices appear, and the flow fields are almost completely two-dimensionalized. The transitions between the Q2D turbulence and the 3D turbulence by changing the system's rotation rate Ω were numerically studied [6]. It was reported that Ro-dependence of turbulent statistics is not monotonic in the range Ro ∼ 1, where the coherent vortices and inertial waves at small wave numbers and the turbulence at large wave numbers coexist [7,8]. The two-dimensionalization and the cyclone-anticyclone asymmetry depend on the external forces and the boundary conditions (e.g., Ref.[9]).Recently, Ref.[10] reported a phase diagram for statistically st...

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Structure and Dynamics of Rotating Turbulence: A Review of Recent Experimental and Numerical Results

Cited by 82 publications

References 80 publications

Rotating turbulence under “precession-like” perturbation

Rotating turbulence under “precession-like” perturbation

Inertial Wave Turbulence Driven by Elliptical Instability

Hysteretic transitions between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence

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